Problem: Simplify the following expression: $\sqrt{45} + \sqrt{80}$
Solution: First, try to factor any perfect squares out of the radicals. $= \sqrt{45} + \sqrt{80}$ $= \sqrt{9 \cdot 5} + \sqrt{16 \cdot 5}$ Separate the radicals and simplify. $= \sqrt{9} \cdot \sqrt{5} + \sqrt{16} \cdot \sqrt{5}$ $= 3\sqrt{5} + 4\sqrt{5}$ Finally, simplify by combining the terms. $= ( 3 + 4 )\sqrt{5} = 7\sqrt{5}$